The paper presents the experimental characterization, the formulation of a numerical model, and the evaluation, by means of non-linear analyses, of a new friction damper conceived for the seismic upgrade of existing building frames. The damper dissipates seismic energy through the friction force triggered between a steel shaft and a lead core prestressed within a rigid steel chamber. The friction force is adjusted by controlling the prestress of the core, allowing the achievement of high forces with small dimensions, and reducing the architectural invasiveness of the device. The damper has no mechanical parts subjected to cyclic strain above their yield limit, thereby avoiding any risk of low-cycle fatigue. The constitutive behavior of the damper was assessed experimentally, demonstrating a rectangular hysteresis loop with an equivalent damping ratio of more than 55%, a stable behavior over repeated cycles, and a low dependency of the axial force on the rate of displacement. A numerical model of the damper was formulated in the OpenSees software by means of a rheological model comprising an in-parallel system of a non-linear spring element and a Maxwell element, and the model was calibrated on the experimental data. To assess the viability of the damper for the seismic rehabilitation of buildings, a numerical investigation was conducted by performing non-linear dynamic analyses on two case-study structures. The results highlight the benefits of the PS-LED in dissipating the largest part of seismic energy, limiting the lateral deformation of the frames, and controlling the increase in structural accelerations and internal forces at the same time.